The continuous evolution in our ability to measure and record complex biomedical data has opened new opportunities, as well as new challenges in the development of evidence based medical care and health management. This application is concerned with complex patient level information, acquired in the form of high frequency functional data (ECG signals, cerebral environment monitors, images, etc.) recorded over several visits or in the setting of medium to long periods of intensive physiological monitoring (for example, Intensive Care Unit settings). We conceptually characterize this information framework as longitudinal functional data. This involves representation of these data classes, in relation to two time scales: historical time, indexing long term changes in the dynamic of processes under investigation, and clock time, indexing short term dynamics. This characterization achieves the goals of identifying sources of variation in the data that are readil interpretable for scientific investigation. We propose a comprehensive holistic development of the theory and methodology for the analysis of longitudinal functional data that span the subjects of regression, clustering and classification and dynamic computation. These developments will provide interpretation and rigorous inference to help guide health care decisions based on complex biomedical data. Even though longitudinal and functional data analysis have established solid bodies of theory and methods, current literature does not yet address analysis of longitudinal functional data with multiple covariates under flexible assumptions. In addition, most applications in the functional data analysis literature involve analysis of data in relatively short periods of time and methods are not directly applicable to medium to long periods of intensive physiological monitoring settings. We propose to analyze these larger scale data sets by the proposed novel longitudinal functional data framework involving chunking longer periods of follow-up into longitudinal units. This is a novel idea in thi literature which utilizes both longitudinal and functional data analysis tools to achieve data analysis in a new level of data complexity. A second element of innovation in our application will consist in the development of fast and accurate algorithms for statistical inference in real time, which will make our methodological contribution ever more useful for clinical and public health applications. We propose three Specific Aims: 1) To develop statistical methods for regression analysis and prediction in the setting of longitudinal functional data; 2) To develop clustering an classification methodology for longitudinal functional data; 3) To develop fast and feasible estimation techniques aimed at online learning in high dimensional settings. These three Aims are accompanied by a fourth exploratory Aim, where we propose to develop statistical methods for time to event analysis using longitudinal functional predictors. Applications for the proposed methodology will include Intensive Care Unit data on traumatic brain injury and cardiopulmonary arrest patients and ERP data in autism spectrum disorder studies.